Journal ArticleDOI
Improved Surrogate Data for Nonlinearity Tests.
Thomas Schreiber,Andreas Schmitz +1 more
Reads0
Chats0
TLDR
It is shown that nonlinear rescalings of a Gaussian linear stochastic process cannot be accounted for by a simple amplitude adjustment of the surrogates which leads to spurious detection of nonlinearity.Abstract:
Current tests for nonlinearity compare a time series to the null hypothesis of a Gaussian linear stochastic process. For this restricted null assumption, random surrogates can be constructed which are constrained by the linear properties of the data. We propose a more general null hypothesis allowing for nonlinear rescalings of a Gaussian linear process. We show that such rescalings cannot be accounted for by a simple amplitude adjustment of the surrogates which leads to spurious detection of nonlinearity. An iterative algorithm is proposed to make appropriate surrogates which have the same autocorrelations as the data and the same probability distribution.read more
Citations
More filters
Journal ArticleDOI
A two-stage linear programming optimization framework for isolated hybrid microgrids in a rural context: The case study of the “El Espino” community
Sergio Balderrama,Francesco Lombardi,Fabio Riva,Walter Canedo,Emanuela Colombo,Sylvain Quoilin,Sylvain Quoilin +6 more
TL;DR: Different approaches to size isolated microgrids are tested, with the conclusion that methods accounting for the uncertainty in both demand and renewable generation may lead to a more robust configuration with little impacts on the final cost for the community.
Chaos theory in hydrology: important issues and interpretations
TL;DR: A brief review of some of the past studies investigating chaos in hydrological processes is presented in this paper, which reveals that most of the problems, such as data size, noise, delay time, in the application of chaos theory have been addressed by past studies.
Journal ArticleDOI
The Nonlinear Behavior of the Black Hole System GRS 1915+105
TL;DR: In this paper, it was shown that the various types of long-term variability exhibited by the black hole system GRS 1915+105 can be explained in terms of a deterministic nonlinear system with some inherent stochastic noise.
Book
Synchronization and Interdependence Measures and their Applications to the Electroencephalogram of Epilepsy Patients and Clustering of Data (PhD Thesis)
TL;DR: A new, conceptually very simple and natural, hierarchical clustering algorithm, called mutual information clustering (MIC), which is introduced and illustrated with several applications and lies in vastly reduced systematic errors, when compared to previous estimators.
Journal ArticleDOI
Testing for nonlinearity in irregular fluctuations with long-term trends.
TL;DR: The null hypothesis addressed by the algorithm is that irregular fluctuations are generated by a stationary linear system and the method is demonstrated for numerical data generated by known systems and applied to several actual time series.
References
More filters
Book
Time Series Prediction: Forecasting The Future And Understanding The Past
TL;DR: By reading time series prediction forecasting the future and understanding the past, you can take more advantages with limited budget.
Book
Nonlinear Dynamics, Chaos, and Instability: Statistical Theory and Economic Evidence
TL;DR: In this paper, the changing structure of stock returns nonlinearity in foreign exchange summary, relation to other work, and future horizons are discussed, as well as the size and distribution of the BDS statistic quantiles.
Journal ArticleDOI
Constrained-realization Monte-Carlo method for hypothesis testing
TL;DR: The typical-realization approach, on the other hand, does not share this requirement, and can provide an accurate and powerful test without having to sacrifice flexibility in the choice of discriminating statistic, and is found to depend on whether or not the discriminating statistic is pivotal.